Every stochastic volatility model assumes yes stochastic volatility. All the stochastic volatility models I have looked into however assume constant volatility of volatility. Empirical research (mostly unpublished) shows the volatilRead more at Collector's Blog »
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Thursday, July 9, 2009
Stochastic Volatility Models
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The models are phenomenological and require input of the parameters and so can never be predictive for all scenarios. Sometimes (as in Hull's book) you find that people use a model such as (if I remember correctly) Black's model (rather than Black and Scholes) and forgive me if I got the name wrong, to model for example products that depend on interest rates (which according to Hull have mean reversion and so are not behaving like a Brownian motion) and somehow this model "works out" or "works better" than the B-S because although not intended for this it makes the right outputs. The point to remember is that all of these models are phenomenological and depend on estimates of the inputs such as "historical volatility" and volatility of volatility, so that they are both of academic interest and of engineering interest (see how well they might work in practice). As an analogy consider turbulence modelling which makes some assumptions to close the equations - it works for some geometries but needs a lot of adjustment or fails for others. So I guess the thing to do is construct and study these models and then somehow evaluate them for different scenarios and issue recommendations as to how and when to use them? More than one model (and quite differently motivated models) may give the same outputs. In recent years ways of speaking in averages (fuzzy logic) have been as effective as complex control theories in practical engineering.
posted 54 minutes ago
I am going to be presenting a paper on Volatility Modeling and Trading at the upcoming Quant USA conference in New York next week in which I discuss a very effective stochastic volatility of volatility model, the ARFIMA-GARCH model. It models volatility as a long memory process which is disturbed by shocks from the volatility of volatility process, which evolves in GARCH form.
The paper evaluates the performance of the model in trading S&P options.
More on the conference here: http://web.incisive-events.com/rma/2009/07/quant-congress-usa/index.html
More details on my Quantitative Investment and Trading blog to come:http://quantinvestment.blogspot.com/